Although I'd want more information to advise you, generally you should run all estate transactions through a separate account.
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You sure do.
The bank generally won't cash a check made out to the estate, even if the administrator signs it. Similarly, they won't allow it to be deposited into a personal account.
An estate checking account is easy to obtain. In addition to your letters of administration (and perhaps a certified copy of the death certificate), you'll only need an estate TIN (taxpayer ID number). I've posted the link below for obtaining this. Doing so should only take about five minutes. Be sure to access the site with Microsoft Internet Explorer and to have Adobe Reader installed on your computer.
I'm sorry, incidentally, to hear of your mother's passing.
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Mr. Ashman is correct in stating that more information would be needed, and that, in general, estate assets should be run through an estate account. If the retirement benefits were actually made payable to your mother's estate, rather than to you or any other individual, then the estate will normally be the entity which pays the taxes on that income, and in that case it would be particularly important to have the money in an estate account initially.
Instead of trying to get specific help in this format, I would very strongly recommend to you that you consult an experienced probate attorney to help you figure out how to handle the estate, if you haven't already done so. Even if you have been appointed administrator and are the only heir, the estate administration process can have a number of confusing areas and pitfalls, and the advice of an experienced attorney is generally well worth the money.
This answer is not intended to provide you with specific legal advice regarding your situation, or to create any attorney-client relationship. The intent is only to provide general information. You should be aware that you cannot rely on this answer to provide you with any protection against tax penalties. You should always consult your own attorney in order to obtain legal advice.